Expected Weighted D-optimal Designs for Experiments with Mixed Factors

TL;DR

This paper introduces Expected Weighted D-optimal designs for experiments with mixed factors, providing algorithms to find robust and efficient designs under various conditions, demonstrated through real experiments.

Contribution

It proposes a new class of robust experimental designs and algorithms for mixed factors, enhancing efficiency and robustness over traditional methods.

Findings

Designs are highly efficient compared to locally D-optimal designs.

Algorithms effectively find EW D-optimal designs with mixed factors.

Designed experiments show robustness against parameter misspecifications.

Abstract

Optimal designs can help experimenters obtain more accurate parameter estimates with reduced experimental time and cost. In this paper, we characterize the Expected Weighted (EW) D-optimal designs as robust designs against unknown parameter values for experiments under a general parametric model with discrete and continuous factors. When a pilot study is available, we recommend sample-based EW D-optimal designs for subsequent experiments. Otherwise, we recommend EW D-optimal designs under a prior distribution for model parameters. We propose an EW ForLion algorithm for finding EW D-optimal designs with mixed factors, and justify that the designs found by our algorithm are EW D-optimal. To facilitate potential users in practice, we also develop a rounding algorithm that converts an approximate design with mixed factors to exact designs with prespecified grid points and the total number of experimental units. By applying our algorithms for real experiments under multinomial logistic models or generalized linear models, we show that our designs are highly efficient with respect to locally D-optimal designs and more robust against parameter value misspecifications.